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Evelyn's apartment complex and the Wayne Commons apartment complex have the same number of apartments. However, Evelyn's apartment complex is built in groups of $11$ apartments, while the Wayne Commons apartment complex is built in clusters of $5$ . What is the smallest number of apartments could each complex have? $\newline$ $\_\_\_\_\_$ apartments

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GCF and LCM: word problems

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Q. Evelyn's apartment complex and the Wayne Commons apartment complex have the same number of apartments. However, Evelyn's apartment complex is built in groups of

11

apartments, while the Wayne Commons apartment complex is built in clusters of

5

. What is the smallest number of apartments could each complex have?

\newline

\_\_\_\_\_

apartments

Identify Problem Requirement: Step $1$ : Identify the problem requirement. $\newline$ We need to find the smallest number of apartments that can be evenly divided into groups of $11$ and clusters of $5$ . This requires finding the Least Common Multiple (LCM) of $11$ and $5$ .
Calculate LCM: Step $2$ : Calculate the LCM of $11$ and $5$ . $\newline$ Since $11$ and $5$ are both prime numbers, their LCM is simply their product. $\newline$ LCM = $11 \times 5 = 55$

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